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Node Node = Point that connected together on the same wire V Example 3 nodes

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Nodal Analysis Procedure 1. Count the number of nodes = N 2. Choose one of the nodes to be a reference node (0V) when there is no ground 3. Give the voltage for other nodes to be V1, V2, V3, … 4. Use Kirchoff’s current law on each node to form N-1 equations 5. Solve the equations to find V1, V2, V3, …

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Example 0V (reference) V1 V2

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0V (reference) V1 V2 Equation 1

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0V (reference) V1 V2 Equation 2

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Solve the Equations V1 V2 V1 = 5 V V2 = 2.5V

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Example V1 V2 V3 0V

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V1 V2 V3 0V Equation 1

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V1 V2 V3 0V Equation 2

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V1 V2 V3 0V Equation 3

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Solve the Equations

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Cramer’s Rule (Optional)

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Supernode When there is a voltage source in the circuit, direct KCL cannot be used because we do not know the current in the voltage source. We will use the idea of supernode. Supernode is the method that combines 2 nodes together when using KCL. It will include the voltage source within the circle when using KCL.

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Example V1 V2 V3 0V

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V1 V2 V3 0V Equation 1

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V1 V2 V3 0V Equation 2 supernode Equation 3

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V1 = V V2 = V V3 = V

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Example 0V V1 V2

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Sanwa YX360TRF Multimeter

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Range Selector DialResistance Zero Adjust

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Resistance Measurement Read this Range Select these ranges

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Voltage Measurement Read this Range Select these ranges

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Current Measurement Read this Range Select these ranges

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Measure the Resistance of Ammeter and Voltmeter Adjust a multimeter to measure volt and use another multimeter to measure its resistance. Adjust a multimeter to measure amp and use another multimeter to measure its resistance.